Local multiscale model reduction using discontinuous Galerkin coupling for elasticity problems

Abstract

In this paper, we consider the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with discontinuous Galerkin (DG) coupling for the linear elasticity equations in highly heterogeneous and high contrast media. We will introduce the construction of a DG version of the CEM-GMsFEM, such as auxiliary basis functions and offline basis functions. The DG version of the method offers some advantages such as flexibility in coarse grid construction and sparsity of resulting discrete systems. Moreover, to our best knowledge, this is the first time where the proof of the convergence of the CEM-GMsFEM in the DG form is given. Some numerical examples will be presented to illustrate the performance of the method.

Constraint Energy Minimizing Generalized Multiscale Finite Element Method for multi-continuum Richards equations

“…Adaptivity can also be performed in the CEM-GMsFEM, as shown in [25,20,21]. Some recent applications of the CEM-GMsFEM can be found in [37,95,87]. With the CEM-GMsFEM's development, there have been important studies on the non-local multi-continuum (NLMC) method [94,82,24,83,84].…”